text: import torch
  from torch.optim import Optimizer
  
  
  class Nadam(Optimizer):
      """Implements Nadam algorithm (a variant of Adam based on Nesterov momentum).
  
      It has been proposed in `Incorporating Nesterov Momentum into Adam`__.
  
      Arguments:
          params (iterable): iterable of parameters to optimize or dicts defining
              parameter groups
          lr (float, optional): learning rate (default: 2e-3)
          betas (Tuple[float, float], optional): coefficients used for computing
              running averages of gradient and its square
          eps (float, optional): term added to the denominator to improve
              numerical stability (default: 1e-8)
          weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
          schedule_decay (float, optional): momentum schedule decay (default: 4e-3)
  
      __ http://cs229.stanford.edu/proj2015/054_report.pdf
      __ http://www.cs.toronto.edu/~fritz/absps/momentum.pdf
      """
  
      def __init__(self, params, lr=2e-3, betas=(0.9, 0.999), eps=1e-8,
                   weight_decay=0, schedule_decay=4e-3):
          defaults = dict(lr=lr, betas=betas, eps=eps,
                          weight_decay=weight_decay, schedule_decay=schedule_decay)
          super(Nadam, self).__init__(params, defaults)
  
      def step(self, closure=None):
          """Performs a single optimization step.
  
          Arguments:
              closure (callable, optional): A closure that reevaluates the model
                  and returns the loss.
          """
          loss = None
          if closure is not None:
              loss = closure()
  
          for group in self.param_groups:
              for p in group['params']:
                  if p.grad is None:
                      continue
                  grad = p.grad.data
                  state = self.state[p]
  
                  # State initialization
                  if len(state) == 0:
                      state['step'] = 0
                      state['m_schedule'] = 1.
                      state['exp_avg'] = grad.new().resize_as_(grad).zero_()
                      state['exp_avg_sq'] = grad.new().resize_as_(grad).zero_()
  
                  # Warming momentum schedule
                  m_schedule = state['m_schedule']
                  schedule_decay = group['schedule_decay']
                  exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
                  beta1, beta2 = group['betas']
                  eps = group['eps']
                  state['step'] += 1
                  t = state['step']
  
                  if group['weight_decay'] != 0:
                      grad = grad.add(group['weight_decay'], p.data)
  
                  momentum_cache_t = beta1 * \
                      (1. - 0.5 * (0.96 ** (t * schedule_decay)))
                  momentum_cache_t_1 = beta1 * \
                      (1. - 0.5 * (0.96 ** ((t + 1) * schedule_decay)))
                  m_schedule_new = m_schedule * momentum_cache_t
                  m_schedule_next = m_schedule * momentum_cache_t * momentum_cache_t_1
                  state['m_schedule'] = m_schedule_new
  
                  # Decay the first and second moment running average coefficient
                  exp_avg.mul_(beta1).add_(1. - beta1, grad)
                  exp_avg_sq.mul_(beta2).addcmul_(1. - beta2, grad, grad)
                  exp_avg_sq_prime = exp_avg_sq / (1. - beta2 ** t)
                  denom = exp_avg_sq_prime.sqrt_().add_(eps)
  
                  p.data.addcdiv_(-group['lr'] * (1. - momentum_cache_t) / (1. - m_schedule_new), grad, denom)
                  p.data.addcdiv_(-group['lr'] * momentum_cache_t_1 / (1. - m_schedule_next), exp_avg, denom)
  
          return loss
  